A HIERARCHY OF MODELS FOR THE ELECTRICAL CONDUCTION IN BIOLOGICAL TISSUES VIA TWO-SCALE CONVERGENCE: THE NONLINEAR CASE

M. Amar; D. Andreucci; P. Bisegna; R. Gianni

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A HIERARCHY OF MODELS FOR THE ELECTRICAL CONDUCTION IN BIOLOGICAL TISSUES VIA TWO-SCALE CONVERGENCE: THE NONLINEAR CASE

机译：两层融合的生物组织中电传导模型的层次：非线性情况

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We study a hierarchy of electrical conduction problems in biological tissues. These problems are set in a finely mixed periodic medium, and the unknown electric potentials solve standard elliptic equations set in different conductive regions (the intracellular and extracellular spaces), separated by an interface (the cell membranes), which exhibits a capacitive and a nonlinear conductive behavior, due to its biochemical structure. Different scalings in the interface condition correspond to different problems in the hierarchy. As the spatial period of the medium goes to zero, the problems approach a homogenization limit depending on the initial scaling. The macroscopic models are obtained by using the technique of two-scale convergence.

机译：我们研究生物组织中的电传导问题的层次结构。这些问题设置在精细混合的周期性介质中，未知电位解决了设置在不同导电区域（细胞内和细胞外空间）中，由界面（细胞膜）隔开的标准椭圆方程组，该界面表现出电容性和非线性导电行为，由于其生化结构。接口条件的不同缩放比例对应于层次结构中的不同问题。随着介质的空间周期变为零，取决于初始缩放比例，问题接近均质化极限。宏观模型是通过使用两尺度收敛技术获得的。

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来源
《Differential and integral equations》 |2013年第10期|共28页
作者
M. Amar; D. Andreucci; P. Bisegna; R. Gianni;
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正文语种 eng
中图分类微分方程、积分方程;
关键词
technique; two-scale; convergence;

机译：技术;两尺度;收敛;

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专利

1. A HIERARCHY OF MODELS FOR THE ELECTRICAL CONDUCTION IN BIOLOGICAL TISSUES VIA TWO-SCALE CONVERGENCE: THE NONLINEAR CASE [J] . M. Amar, D. Andreucci, P. Bisegna, Differential and integral equations . 2013,第9a10期

机译：两层融合的生物组织中电传导模型的层次：非线性情况
2. Exponential decay for a nonlinear model for electrical conduction in biological tissues [J] . Amar M., Andreucci D., Gianni R. Nonlinear Analysis: An International Multidisciplinary Journal . 2016,第Null期

机译：生物组织中导电非线性模型的指数衰减
3. Asymptotic decay under nonlinear and noncoercive dissipative effects for electrical conduction in biological tissues [J] . Amar Micol, Andreucci Daniele, Gianni Roberto Nonlinear differential equations and applications: NoDEA . 2016,第4期

机译：非线性和非矫顽耗散作用下生物组织中电传导的渐近衰减
4. Electrical Conduction in Biological Tissues: Homogenization Techniques and Asymptotic Decay for Linear and Nonlinear Problems [C] . M. Amar, D. Andreucci, P. Bisegna, International Conference on Simulation and Modeling Methodologies, Technologies and Applications . 2013

机译：生物组织中的导电：线性和非线性问题的均质技术和渐近衰减
5. In vivo electroporation of skin and biological tissue: Theoretical model development and numerical investigation of associated thermo-electrical and structural responses and enhanced mass transport. [D] . Becker, Sid. 2007

机译：皮肤和生物组织的体内电穿孔：理论模型开发以及相关的热电和结构响应以及增强的质量传递的数值研究。
6. Modeling the collagen fibril network of biological tissues as a nonlinearly elastic material using a continuous volume fraction distribution function [O] . Reza Shirazi, Pasquale Vena, Robert L. Sah, -1

机译：使用连续体积分布分布函数将生物组织的胶原纤维网造型为非线性弹性材料
7. On a hierarchy of models for electrical conduction in biological tissues [O] . M. Amar, D. Andreucci, P. Bisegna, 2012

机译：在生物组织中电传导模型的层次结构中

A HIERARCHY OF MODELS FOR THE ELECTRICAL CONDUCTION IN BIOLOGICAL TISSUES VIA TWO-SCALE CONVERGENCE: THE NONLINEAR CASE

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